Do we live inside a mathematical equation?
February 18, 2013
(Credit: iStockphoto)
Reality is a mathematical structure, says MIT physicist Max Tegmark — his “mathematical universe hypothesis,” reports Science Now.
“If the mathematical universe hypothesis is false, that means that the future of physics is ultimately doomed,” says Tegmark. However, “if the mathematical universe hypothesis is true, we can actually learn things about the parts of our universe we can’t see or visit. … The road ahead is open, and our future understanding is really only limited by our imagination.
“We’ve discovered again and again that reality is bigger than we thought…our whole observable universe is just … part of a much bigger space, with lots of parallel quantum realities.”
Comments (95)
by Matt Montgomery
There is a related KurzweilAI article about Jürgen Schmidhuber’s ensemble of computable multiverses. Tegmark and Schmidhuber published their first papers on this in 1997 when they were both based in Munich.
Schmidhuber emphasizes computability and computational complexity. He even uses this to make predictions. So his theory is falsifiable, to an extent.
He also gives credit to his brother Christof Schmidhuber, a string theorist. He says he suspects Christof’s earlier ideas on the “universe as the sum of all mathematics” are the real reason why such ideas emerged in Munich. Check it out: http://www.kurzweilai.net/in-the-beginning-was-the-code
by Scott
Here’s a question: Why are we here? Say we do live in a mathematical equation or a simulacrum, but why? Are we entertainment for something/someone?
by thinkahol
My guesses are as an experiment or as a passing of the torch (so to speak). There are countless reasons we experiment, one of which is to help us figure out our own origins. And by “passing of the torch” i’m reflecting on valuing life. We now know that our universe is unstable, and it seems like it would be approaching heat death anyway. What if in in creating new universes we could expand time within them (even if only experientially).
by anon
Everything in mathematics can be reduced to 0 and 1, nothing and something, as the computer you’re using demonstrates. Can you imagine a universe that doesn’t have those two things?
It seems that when you take everything else away those two things are what’s left, hence nothing else really exists.
by SmartAndSober
There are more than the *0-1* (Binary) method to reduce Mathematics to.
If Charles Babbage’s Decimal Computer (which used *0-9*) became mainstream, we would probably say that “Everything in Mathematics can be reduced to 0 to 9″.
by anon
Yes, but is there anything less you can reduce it to?
Nothing and half, 0 and 0.5 perhaps? (What is half? What is half of something? Is it neither nothing nor something? Is it both nothing and something?)
Or nothing and infinitesimal 0.0000…1 (where ‘…’ is infinity) or 0.999…
In any case you can represent them as nothing and something. Something can be anything, anything except nothing, so anything can represent it. Nothing can be represented by anything also, but absence of something (whatever it is) is usually practical.
by Rob Falgiano
I agree. Any anything more complex than 0 or 1 can simply be expressed as a string of binary numbers. It occurred to me that the universe “on paper” is a nearly (or actual) infinite number made up of zeros and ones in succession. And the relative abundance of zeros or ones and accompanying patterns account for varying degrees of complexity. Does this make sense?
by Bri
The smallest unit for describing something has to be two of something. If you have only one it is static. What you call the two rescinding elements is just the language that you use. Mathematics is just a language. It uses symbols to describe relationships. Me personally I prefer Yin and Yang. It’s just a graphic of ones and zeros. Another symbol that represents the same thing. Whether you say that reality is a mathematical simulation or a holodeck, you are saying the same thing. What it boils down to is energy being bond to a relationship. Take away the energy and what you have left is the concept. I refer to that as spirit. When our universe comes to it’s end and time and space no longer exist, as Roger Penrose’s latest theory explores, those concept still exist. It’s just that there isn’t any matter to express them in. The concepts are eternal. In infinite time all of them will repeat endlessly. Time becomes irrelevent. That is why your spirit is eternal. This reality is a manifestation of concepts or spirit. Even energy itself is a concept from spirit. That realm of spirit is what we call heaven or god. All the infinite possibilities exist there, they just aren’t manifest. As soon as you separate just one concept and manifest it, you create a need for time and space. It must have a beginning, and if it has a beginning it must have an end. In the Hindu language it is refered to as Brahma, Vishnu, and Shiva. The lords of birth sustenance and death. They are anthropomorphized because consciousness creates them. Without the observer what exists? I Am….. That…. I Am. We are tiny fractions of that “spark”. All of everything together is god.( I know all things, I am all things, as Mc Cloud says in The Highlander) nearer than hands, nearer than feet. Even every speck of nothing is pregnant (potential) with everything. Nothing is god experiencing or knowing not knowing or unconsciousness. They are opposite sides of the same coin, or Yin and Yang that is the holodeck. To get to the other side you have to observe the observer. To do that you have to stop observing your manifestation in this plane of existence. Suspend your existence and you revert to your primordial form. The center of an infinite circle. The uncollapsed wave function. All possibilities. Your physical body keeps trying to call you back unless you learn how to unmanifest it. Then you can send it anywhere through what we refer to as worm holes. That’s what the EPR effect or entanglement gets it’s spooky action at a distance from. Time and space are just an illusion that we all create together. It’s a room full of mirrors. There is only the one.
by anon
It does. So is there anything simpler you can build stuff out of? If not, doesn’t it mean that we’re built out of that, 0 and 1, nothing and something, being and non-being, two different things whatever they are?
by Rob Falgiano
I suppose so, but I’m not smart enough to take the idea any further than I already have :-)
by asiwel
This article certainly generated enough comments! I would add only a recommendation to take a look at an amazing book published in 2011: BEYOND PERMANENCE: THE GREAT IDEAS OF THE WEST by Craig Eisendrath, which I believe may have been reviewed here on KurzweilAI.net. This story book begins with the ancient Sumerians and the Epic of Gilgamesh, goes through all or most of the major Western philosophies of science and religion since then, and winds up concluding with a lengthy and thoughtful discussion of the ideas of Werner R. Loewenstein and Ray Kurzweil! That surely covers a bit of fundamental “ground,” so to speak, but almost all of Eisendrath’s thesis and selected topics reflect directly on the comments here about a “mathematical reality” hypothesis.
by Jim Mooney
Physics may be doomed, but how do we know where math will go? One day advanced math may be couched in terms of music. Isn’t that how it started, with the study of musical ratios? What equations are Beethoven and Mozart making? When flying aboard a KC-135 many years ago, which is unshielded to jet noise, the white noise gradually turned into classical music in my head. Oddly, I had no taste for it at the time. Why not pop or Beatles? Classical really could be the Music of the Spheres.
by SmartAndSober
Physics can never be doomed.
In 1875, when Max Planck was only 17, he chose to study Physics.
The Munich physics professor Philipp von Jolly advised Planck against going into physics, saying, “in this field, almost everything is already discovered, and all that remains is to fill a few holes.” (From Wikipedia)
Whenever we think everything is already discovered, we are almost certainly wrong.
Here are more good examples of experts’ (pessimic) predictions that end up wrong:
http://www.rinkworks.com/said/predictions.shtml
by Heikos
Sounds correct. Though we can’t predict it to be almost certainly wrong in the future, as we don’t know if it is possible to know ‘everything’. And even if it is possible, how far away that point is.
Predicting that predictions are often wrong, seems to speak against itself.
by SmartAndSober
Positive/constructivist predictions are often true.
First of the Arthur C. Clarke’s 3 Laws:
When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong.
by Klaatu
Physics is not doomed…I have confirmed that fact with
the Intelligent Designer herself.
by Mortran
This is exactly the same theory that Pythagoras had 2500 years ago.
by Leonardo Arenas
There is the ‘Ultimate Knowledge” that is beyond human knowledge (science, mathematics nature’s physics, contemporary technology, human philosophy, psychology, logic, quantum mechanics genetics engineering, space/cosmic projects, etc., etc,. you name it…) Human knowledge is just so limited by what the human faculties can access to generate new ideas, inventions using his limited knowledge, experience education and so forth. All these ideas and inventions only relate to his physical environment that his faculties can reach, sense and imagine. If man want’s to expand this limited knowledge, he must “connect” to the originator of this “Ultimate Knowledge” – One who created him and the ‘infinite universe’
by Rhadji
Do you “know” this ‘Ultimate Knowledge”??
by MatthewQ
He actually said in his comment that he did not (assuming he’s human).
by SmartAndSober
“… he must “connect” to the originator of this “Ultimate Knowledge”… ”
I believe that *connecting* to cyborgization parts that enhance our cognitive abilities is a better solution.
by Bri
I’ve been holding off on this type of line of reasoning. What is the observer? We talk about augmentation and some of Leonardos post references this. There is so much that we don’t experience. Can we experience everything? Can mathematics represent any infinity? Was the infinite always there and if not, how did infinity come into being. If we manage to ” live forever” does our consciousness become infinite? I think all of this lies well outside the abilities of any mathematics. Mathematician and physicist don’t like infinities. They generate nonsense answers. There is no practical way to relate to something that has no boundaries.
by SmartAndSober
Our hope (for achieveing True Omniscience) lies in the Omega Point.
Frank J. Tipler believed that In the far future, We will convert the Whole Universe into a Supercomputer (and We will Merge with that Supercomputer). Through some form of Esoteric Physics, It is possible to make this Universe Supercomputer to Perform Infinite Computation with Finite Energy And Within Finite Time. If that happens, we will Achieve Omniscience.
by Bri
It’s a debatable point if a finite can ever reach true infinity. Even the sum total of this universe would disappear in relation to a true infinite, but I do like your choice of reasoning. We still have to deal with that heat death of the universe thing. Though I do take comfort in multidimensionality/ string theory stuff. Not to mention the multiverse.
by SmartAndSober
Thanks for the reply. I speculate that, even after we achieve the Omega Point (if finite Can achieve infinity, then we probably won’t take the whole Universe), the vast *Intelligence* and *Knowledge* we gain will still dwarf in comparison to some Even Greater Form of Infinity.
(Mathematician Georg Cantor invented the concept of “Transfinite”: Some Infinities are Greater Than Others.)
For example, the Infinite Set of all Real Numbers is Much Larger Than the Infinite Set of All Integers.
Perhaps a Universe-wide (Cosmic) Omega Point is a prelude to some Even Greater (Multi-Cosmic) Omega Point.
by SmartAndSober
I want to quote Rick Cook about Omega Point:
Tipler’s God at the end of the universe is no scowling Yahweh or thunderbolt-slinging Jupiter, or even kindly, gentle Gaea. His Holy Spirit is the universal wave function of quantum mechanics, and his God is the most super of all the supercomputers, an information-processing construct that literally encompasses the whole universe.
by Jeanne
Sometimes it sounds as if the theorist is simply describing his/her own mind. Is there more?
by SmartAndSober
After I have thought repetitively about Omega Point Theory, I find it not satisfying. “Subjective infinite lifespan” is not *real* infinite lifespan.
I recommend people to Google “Linde’s Scenario”.
Linde’s Scenario involves escaping or expanding into other universes (provide that such other universes exist).
by SmartAndSober
I have a little question. Universe *must* follow mathematical laws.
How can *any universe* exist *without* such laws?
by SmartAndSober
I am reminded of what Carl Sagan mentioned in the end of his novel Contact.
He speculated the possibility of a message buried inside the value of pi, the ratio of circumference to diameter of a circle.
THat, to me, seems to suggest that Pi can be of a different (slightly so)
value (picked by the Creator of Universes, who also enbeded the message).
But, I fail to imagine how could Pi take on a differnet value.
I mean, I fail to imagine how could a cirlce, in another universe, have a different circumference to diameter ratio other than 3.1415…?
(Or, expressing Pi using the Gregory series, 4 times the sum of all (infinite) nature number Ns in (-1)^(N+1) / (2N-1).
I can imagine universes in which the Periodic table is different (different number of clumns and rows), the mass of proton is different (or even, populated by a set of totally different elementary particles), or the quarks do not carry 1/3 or 2/3 of electromagnetic charge but a different rational number.
But I simply cannot imagine how could mathematical constants be tweaked.
(Or even, a universe *without* mathematical rules. Will rules *spontaneously emerge* in such universes?
Or perhaps such rules are *not* fundamental to existence?
I mean, could anyone here imagine, and tell the rest of us how to imagine, a universe without mathematical and logical rules?)
by Dan Robinson
If I understand right, such a message, and all others, have to be buried within pi, if you search far enough, know what you’re looking for and your computer can reject all close similarities.
Is pi perhaps dependent on the curvature of the universe, as in circles drawn on the surface of the earth, and we locally only see a very small example of that curvature here? Then designers of different universes could have different messages prominently displayed. But how could such messages be accurately converted to meaningful information?
by SmartAndSober
Thank you for the reply, Dan.
“(Pi is) perhaps dependent on the curvature of the universe”.
Thanks for telling that idea.
I am reminded of the (very much cliched) analogy of *inflation of Universe* to the inflation of balloons. But, of course, that is not a very accurate analogy, because the universe is a *sphere-equivalent* in the a 4-dimensional space (the “Multiverse”).
But, there is a more *absolute* definition of Pi:
Given the coordinates a point O (on a idealized, perfectly flat 2-dimensional plane) and a certain distance (N units), plot all points being N units away from O.
These points should form a closed curve: a circle (a perfect circle unaffected by any *space curvature* of the physical universe).
A circle in the physical universe is *not* perfect because of the aforementioned curvatures (of the surface it is drawn on and of the universe) and the fact that space is *pixelated* at Planck-scale.
But a mathematical idealization is perfect. And the conventionally known Pi (one obtainable from the Gregory series and other infinite sum series or infinite product series) is the circumference-to-diameter ratio (Pi) obtained from such a perfect circle.
by SmartAndSober
“… because the universe is a *sphere-equivalent* in the a 4-dimensional space (the “Multiverse”).”
I wish to add: In the “balloon” analogy, the universe is a 3-dimensional object (a sphere) with 2-dimensional entities (galaxies, stars and other structures) located on its surface. But it is (at most) an analogy, not an accurate description of the topology of *our universe*.
Our universe is a *sphere-equivalent* in a 4-dimensional space.
This is similar to how, in a 4-dimensional universe*, a *hypercube* is equivalent to *cube* in the 3-dimensional universe. (For more info on hypercube, please read en.wikipedia.org/wiki/hypercube )
Despite being *equivalent* (perhaps, in Formal Mathematics, the mathematicians use another adjective), a *hypercube* is *very* different from a 3-dimensional cube.
For example: a *cube* consists of 6 *faces*, but a *hypercube* have 8 *face-cubes* (Hypercube is a 4-dimensional “Polychoron”, its equivalent of faces in a 3-dimensional “polyhedron” (in this case, cube)).
This is the precise reason I said “this is not a very accurate analogy”.
by ARaiken
I think you answered you’re own question. You said “I can’t imagine it.” Perhaps that is what limits you. Each Universe would be it’s own construct. The rules don’t exist outside of each one. They are not dependent on one another for their existence. What you’re trying to describe is a grain of sand in the desert of possibility.
by CharlesH
Not that I take the “message embedded in Pi” seriously, to to answer your implied question of “But, I fail to imagine how could Pi take on a differnet value.”, you need to realize that the traditional value of Pi doesn’t apply to this universe. The traditional value applies only to a flat space-time. When space-time is bent, the value of Pi that applies changes. And we live in a bent space-time. Also note that it’s bent in different degrees at different locations, from inter-galactic space, to near a black-hole. So the value of pi isn’t constant over the universe.
by SmartAndSober
Another interesting question:
Can we tweak the constants and equations that govern our universe?
If our universe is simulated by a computer, can we hack that computer (from inside)?
The last suggestion is featured on the 10th entry of Eliezer Yudkowsky’s Ambition Scale (http://lesswrong.com/lw/ehd/the_yudkowsky_ambition_scale/).
by Rob Falgiano
That is an interesting notion. You’d have to be nearly godlike to hack the universe computer. I’ve speculated that advanced civilizations that have come before us may have had the same notion, but for some reason they have apparently not succeeded. Or were not allowed to succeed. Looking back through time with our telescopes shows consistency in universal physical laws.
by XLife
That would make sense since many programmers think they’re God.
by SmartAndSober
A deist god perhaps (a creator), certainly not a theist god (a supervisor).
by joe lanyadoo
all universes mast have mathematical formulas…everything is a program…first god created everything using mathematical and chemical formulas…then he created four letters from 4 complex molecules, he then converted those formulasto words…god inot a magacian but a program writer…he created us by letter combinations -the word…4 DNA letters which he combined to create all life.
Sun: MC2 describes how the sun makes energy. Replacing Hebrew letters to Einstein formulas. MC2 = MCC =שמש=משש Sun in Heb. The numerical value of the letter C-Shin is 300 which is identical to the speed of light(metric). Einstein decoded correctly the Hebrew word for sun…. accident? magic?….or Just a science we don’t understand…it also explains why Einstein insisted on C for the speed of light, because it stands for the speed of light in Heb, otherwise the formula wouldn’t work (I am not suggesting he knew that). The letter M in the formula cMc means hydrogen/water or Mass (all the same-1). The letter looks like a wave.
Water H2O spelled out HOH,…. מימ = hoh = m.y.m water in Heb . The מm stands for hydrogen. O in the formula corresponds to the Hebrew letter י Yod in מימ which stands for Yhwh. Oxygen is a god over life and has 2 orbits of 2-6 electrons which not coincidentally the same as the numerical value of Yhwh-26. The Hebrew word חמצן meaning Oxygen is numerically 8+4+9+5 = 26. …and then god mr 26 planted 26000 genes…
theoriginoflanguage.com
by SmartAndSober
This sounds like a bit too weird, but I speculate that:
If there is a supernatural God, and what you claimed (math/physics laws correspond to Hebrew letters/words) is true, than the intervention necessary for this to happen would be:
God guiding/tweaking the evolution of human culture/languages so that
a group of people start speaking language with the *cosmic constants* (math/physics constants and equations) correspond to the vocabularies.
Actually, a cosmic-creator God is not required to achieve this.
Some intelligent aliens or even prehistoric human civilizations could do this. (If these aliens or humans had knowledge of science and intervened human culture).
In other words: physics are not modified to correspond to human language.
Human languages are modified to correspond to physics.
We have to clarify on the causality.
by MatthewQ
What if there are no supernatural gods? Just natural ones?
Serious question: What would natural (non-supernatural) gods pray to?
What would a Turing test for godhood look like? Would the test look different depending on the level of the species administering it? I think it would. So, like the term ‘primitive’ the opposite term ‘god’ is a relative term.
I went throughMax Tegmark’s website last night, searching for more. Read his papers. Interesting stuff. He’s pushing extreme Platonism. He has a ‘questions’ page and one of the questions had to do with the relative nature of god. His answer was interesting. He acknowledged that such creatures might exist in his Level IV reality.
Personally, I think, depending on how you defined the term, they almost certainly exist in our own (Iain Banks-like ‘Minds’ from his Culture novels or something similar to Q from Star Trek). Maybe even in our own galaxy.
I have been a believer in such a Level IV reality most of my life. I have never worked out in my head whether it implies a creator or not. I am agnostic on the question. But I always remind myself- based on the sliding scale Turing test for godhood- I wouldn’t know the difference in ‘THE god’ and just a mere ‘god minus 1′. It’s a moot question. We’ll never break through our own local membrane to be able to properly investigate the problem.
We can only hope that if our own existence happens to be running on the equivalent of an MP3 player of some hyper-dimensional teenager he’ll remember to keep the batteries charged and not delete us in favour of the latest music craze.
by Rob Falgiano
I feel certain that a Q-like intelligence is an inevitability given enough time for a species to evolve to that level and/or merge with its technology. The interesting question for me then becomes: What does a Q-like intelligence crave? And would a Q-like intelligence discover that immortality is not necessarily a blessing? That mortality forces urgency upon life…
by MatthewQ
“I feel certain that a Q-like intelligence is an inevitability”
Me too.
I remember how awed I was when I first encountered the idea of an advanced species building a Dyson Sphere around a sun. Then one day the thought struck me- what about a being who could build a Dyson Sphere around a galaxy? And that idea is, of course, further recursive by taking the idea up one more notch to include our entire Hubble Volume. It actually makes me shudder in awe/fear/dread to take that idea any further than that.
An explanation for the ‘dark matter’ we are missing? ;-)
by SmartAndSober
” Dyson Sphere around a galaxy… ”
I believe building multiple Dyson Spheres around every (or most) stars in a galaxy is a more optimal solution. It would be more flexible (you can move the stars and change the overall shape of that galaxy easier).
If a Dyson Sphere also functions as a *star-mover* (please Google “Shkadov Thruster”), then stars can be moved at the will of intelligent beings.
Perhaps the *disk-shape* is not the optimal shape for galaxies.
Supercivilizations can probably reshape their galaxy (or multiple galaxies) into a more de-centralized shape (instead of having most matter and the supermassive blackholes concentrating in the *galactic-core* and the galaxy being a disk with the rest of *spherical-volume* unpopulated, the galaxy can be modified to a more homogeneous shape).
by MatthewQ
Ya, my comment was more pointing towards the ‘awesomeness’ of a creature who could actually accomplish this. Not really that there would be a legitimate point in doing so. I like to imagine things like ‘god’ being a membrane that contains the universe- it can access all the information within and all the constituent parts inside amount to organelles inside a cell. And then, you have enough of those tied together to make an organ. Then a lot of organs making an organism, species, society.
I love thinking about these things but when you get on those lines of thought it’s always recursive into infinity and it starts to unravel your mind.
This is the ‘disturbing implication’ of the Level IV multiverse/reality. If a mathematical construct that describes such a thing exists- then that thing exists. If you can write the code for a god dribbling a universe like a basketball, it exists. As long as the math is consistent.
I enjoyed your post. Thanks.
by H.K. Fauskanger
Wow … cabbala meets Einstein! Not sure it does justice to either …
by WeakestLink
It is held together by asterisks.
by Bri
Mathematics is a language. It is a very pure relational language but it only describes those relationships. You can’t take a language by itself and make something. So what does it describe? We can describe the relationships of massless particles but we still don’t know what they are. I was listening to Roger Penrose the other day in a radio interview. He was trying to get across that we can describe a massless particle but we have no idea as to what that really is. He said for now we just think of it as s point in space that has these properties. He was being interviewed in relation to his new thesis on what might have been before the big bang. To do this he walked us through the death of the universe. He said that at the end there is no time and space anymore. There is nothing there. It’s all been ripped apart and no long has a relation to anything. From this nothing a quantum fluctuation starts the whole process again. He said he worked out the mathematics in relation to certain structures in the afterglow of the big bang. This is just his new theory and he was quick to point that out. Mathematics is just a language and you can say nonsense with it just like any other language. The Judeo Christian religious concept is just their theory of god and mans relationship to that concept. We have no more proof of gods existence then we have proof of his none existence. If we assum that our consciousness will continue to grow what stops it from becoming god like? Extrapolate backward and forward, not to mention in every other direction. There has to be something else beyond the boundaries of our existence. I’d leave god out of the discussion. In my view there is more than enough room for a more refined theory of super consciousness than what has been described in past religious concepts. Even with the best math that we have we still don’t know what it is that it describes so well. It’s only woods.
by Dr. Richard
Kurt Godel proved that mathematical systems are generated from mathematical entities that we cannot prove are true, but know are true and drive the logical struture of the system. Either the mind is beyond mathematics, or mathematics is beyond the mind. God is no more a delusional belief sytem, than the person saying it, is his mothers delusion.
by SmartAndSober
“Either the mind is beyond mathematics, or mathematics is beyond the mind.”
I wish to point out that a *mind* is housed by, and depends on, a *brain*.
And that a *brain* is a physical object, that follows physics/mathematics/logic.
Therefore, mathematics is beyond mind.
But, many people (including me) feels that sentience and consciousness have a profound (and cannot be described by ordinary language) quality that make it somehow *transcendent* (beyond the physics/mathematics).
Our mind is confined by the laws/physics/math at most times, but sometimes we can accomplish extraordinary physical feats (like stunts requiring mental concentration and determination) and intelligence/creativity feats.
So, now that we have relevant reasons to believe in both (simultaneously) that physics/math-is-beyond-mind and mind-is-beyond-physics.
I think we should *not* think in the (exceedingly simple) “either A or B” model, but should be more thoughtful and know that “both A and B are partly relevant”.
Knowing that, we should then proceed to *carefully* analyze the truthfulness and non-truthfulness of the 2 concepts.
In this example, we can study how the physical condition influence the human mind/intelligence. Examples could be how diet, drugs and circulation affect human brain performance.
We can also study how mental concentration and determination can help human do extraordinary physical and mental stunts.
Also, we can perform intelligently arranged study on hypnosis, meditation and faith-healing. How suggestions, sometimes even unconsciously recieved, can change human body in a strong, macroscopic way.
Results of these studies can do incredible benefits to the humanity.
by Aaron
Mathematics is a continually expanding toolset for modeling reality on paper. The better the model, the better the predictions. So all you’re really saying when you say the universe is mathematical in nature is that the tools we’ve built work, and if they don’t we’ll invent new ones that do.
by SmartAndSober
There could be universes (at least in imagination) that is *not* based on mathematics.
I guess, in such universes, intelligent beings will fail to build *mathematical* tools. They would need a different set of tools (which I fail to imagine even the most basic property of such tools) to understand the working-principle of their universe and take advantage of them.
by Jod
the mathematical universe hypothesis is true but it’s also not true because there are things that exist in the universe..and there are things that don’t
by joseph
of course, none of these comments take into consideration the simulation argument by bostrom
by Camaxtli
If we are in a simulation, its likely that the universe producing our simulation is also simulation. Its turtles all the way down. Untestable, not interesting.
by MatthewQ
Not interesting to some.
by AZryan
If it’s not testable, how long can you remain interested?
by arch1
Hard to say, but certainly no longer than the simulation operator keeps the simulation running (*and* you in it).
by MatthewQ
By having an imagination?
Your question is a bit like ‘I don’t like apples, how can you like apples?’
My mind is different than yours is all.
by SmartAndSober
Are we capable of creating such a simulation? Should we, if we are capable of doing so?
Then, can our creations (beings simulated by us) create another simulation?
Is there a *peak* of this *simulation-in-simulation* turtle-mountain?
(I mean, because complexity of a simulated-universe cannot exceed the the computational-capacity of the computer that house it, and the capacity of that computer is limited by the laws-of-physics of the external universe, and if the external universe is also a simulation, than it is likely the laws-of-physics is also related to the limits of the (again) capacity of the computer that house it, and so on. There would be a (final-level) universe in which the beings inside it cannot create any furthur simulations.)
How should we behave (our behaviors are presumably monitored by our creators) so that we minimize our chance of being “terminated” (and hence survive longer) if we *do live* inside a simulation?
by Tyler Dresden
The information band width of our universe seems to be the speed of light squared. The container of our universe would need to have a Higher information bandwidth. matter at the speed of light would be stationary in time, The higher information bandwidth would probably be C time the square root of 2
by SmartAndSober
“The information band width of our universe seems to be the speed of light squared.” I find this interesting. May you, Tyler Dresden, give me (and the rest of us) more information on the “information band-width”? Thank you.
by Rob Falgiano
We should behave by being interesting. By having expansive thoughts, and promoting new ideas and ways of looking at the world that make life more meaningful and joyful. I believe there is a moral component to existence and that joy is in fact preferred at the cellular level for longevity and health.
by Ale
This kind of though we know is called reductionism. Tegmark tell us that the Whole can be reduce to electrons: “all the properties that electrons have are purely mathematical. It’s just a list of numbers. So in that sense, an electron is a purely mathematical object”. It’ s true, but…we are sure to distinguish electrons each other? there is a principle called “identity of indiscernibles” first explicitly formulated by Wilhelm Gottfried Leibniz, that states two objects sharing the same properties are the same object. In classical physic two object are easily distinguishable and seems also in quantum physic (where the principle had its glorious moment until 2006 with an article of French…see stanford encyclopedia of philosophy). But now Tegmark reduce all to mathematical objects, and these, I think, are not so easily distinguishable each other. I think more work need to do in this way before have a new theory of the Whole
by Anthony
Reductionism has helped been very helpful to humanity.
Three cheers for reductionism!!!
by Ale
are you sure ? racism too is reductionist. I think it’ s not so good.
by Joe
How is racism a reductionist philosophy?
by Ale
Reductionism deny the pluralism of identities. Reduce the plurality to only one criterion: ethnos, culture, religion… This was and is today too the persuasion of uniqueness, of superiority, regarding one civilization , one culture, values and principles.
by SmartAndSober
Perhaps I am wrong, but I guess “theory of the Whole” means:
A framework (and perhaps classification system) for studying the *emergent properties* that appear when multiple “mathematically simple/trivial” objects (such as particles and fundamental forces in physics) are in vicinity and are potentially capable of interacting with each other. To me, this somehow resembles the studying of patterns within cellular automata.
If my interpretation is not the same as yours, Ale, please correct me.
I will be glad to hear from you. Thank you.
by Mats Svensson
How come im so bad at math then?
Must be a pretty shitty equation.
by Camaxtli
What would be a great boon for humanity are ways of enhancing ourselves so that we have a much more intuitive, visceral grasp of the mathematical relationships that form our universe then most of us currently possess. So much of our understanding is visual, auditory, tactile, but so much of advanced mathematics cannot be mentally visualized by most people, so it always remains something apart, not internalized in the way that you can say, instantly understand the feel of an orange’s rind when asked to recall that sensation.
Like Kurzweil and others have often pointed out, mathematics is just not natural for most human beings. And there are so few in the world who really have a fundamental grasp of mathematics, especially when applied to physics, that the total brainpower devoted to answering the big questions is really tragically underutilized.
by Anthony
Yes! Since I started my doctoral program in education, I have been considering this problem of how to develop an intuitive understanding multivariate mathematical relationships – not just for children – but for adults as well. I spoke with one of my professors about this problem. She said that it is really impossible for humans to visually represent (or intuitively understand multivariate relationships) “we just have to trust that the math is true”. It is also disturbing to realize how many of our cognitive biases prevent us from possessing an accurate understanding of reality. To gain an accurate intuitive understanding of math and the rest of reality, we really must augment ourselves.
by Camaxtli
Could it be possible to convert a multivariate mathematical relationship into a pattern of physical sensations. Where perhaps each input relates to a particular sensation that we can distinguish from another sensation, with multiple inputs producing a unique combination that our brains can connect to the actual mathematics. Like maybe, cold-orange-loud or pointy-green-soft. It might not necessarily be exact, but it would give a feel for that particular set of mathematical information.
by Anthony
I don’t know if it is possible. But I hope it is. A few years ago, I remember watching researchers physically walk into a computer simulation of data sets in a large machine. I believe they were at a university in California. This simulation is the closest thing I’ve seen to my dream of “swimming” through data. They also moved through 3D models of cells, the solar system, and the Milky Way.
by Aaron
Why reuse existing sensations? Why not create new ones. Surely with as many neurons as exist in a single brain, there’s room for new sensations. I remember an article (sorry no link) a while back that mentioned giving rats the ability to see new colors through gene therapy. They were able to learn to use the new color as if they had always had it available. Maybe we can do the same with higher-level sensations?
by Hopper
I’m not sure if this is the link you’re looking for, but I believe the same concept applies.
http://www.kurzweilai.net/neuroprosthesis-gives-rats-the-ability-to-touch-infrared-light
This is what we as humans try to do. Take information and try to realize it it terms we are comfortable with. This is the driving motivation behind models.
So, if at some point we are able to input numerical values as a paticular sensation in our brain, instead of “doing” mathmatics, we’d be comprehending it’s very nature.
by SmartAndSober
I am reminded of the theory (adhered by some scientists) stating that:
biological brains (those of animals) utilizes quantum mechanics and is (at least partially) the basis of some aspects of human intelligence.
If this theory (or other similar theories) is true, we will know that human brains are *at least partially* quantum computers and, with proper trainings (or even physical augmentations, such as cyborg-izations) we can exploit the powerful *quantum computing*-enabled abilities (which is supposedly more powerful than classical computers).
It would be great if developers of augmented-reality hardwares can include (pre-install) graphic-calculator-softwares in their new products.
I as well think that we need a new company (or perhaps non-profit group) to manufacture and distribute (preferably in large numbers) graphic calculators similar to TI-83, but priced much lower than available TI-83 products (which, in my opinion, are very over-priced).
Distribution of low-price graphic calculators would greatly benefit not only education, but also enpower people daily lives.
Perhaps *Grassroot-based* self-motivated science projects will increase in numbers because of such low-price graphic calculators.
The quality of their research can also be improved (if machines that produce mathematical graphs can be of a lower price and become more ubiquitous).
by Deb
Einstein also said “God is a mathematician.” I thought that our reality being math based was already commonly understood. Is Tegmark really the first person to speak about this? I find that even harder to believe than my being a mathematical equation writ wild.
by MatthewQ
You’d be surprised. I’ve been trying to explain this idea to people my entire life and they normally look at me as if I’m crazy. It occurred to me when I was young. A complex enough equation would believe itself to be sentient. You extrapolate that idea and after a while it becomes obvious that the entire universe could be just one big equation and your own consciousness is just one tiny function within it reacting to and interacting with other functions within it.
People seem to balk at the ‘But an equation isn’t really REAL’ (whatever that means) but you always have to keep in mind, from within the equation all your interactions are valid because they are constrained by their own local interactions with the equation and not the overall nature of the equation itself. Your area in the equations is solid to you because you are described by the same functions that describe your electrons and quarks. This is obvious yes?
This idea has always been a happy one for me because it allows one to think about a multiverse without getting bogged down with the sheer size of it. Equations can exist in parallel. They don’t take up any theoretical room at all. No part of the equation need exist until you examine it- this is just another way to describe quantum mechanics.
I’m probably just crazy but you don’t need any formal math training to work with this idea either. Functions within the equation work like gears and cogs in a mechanism. It’s not difficult to then imagine stepping back and seeing a vast and complex machine- you don’t need to be a mechanic.
I’ve always been disturbed though by one prediction of this idea:
If a math exists- it describes a part of the universe. It must. This is an intuitive idea for me but it is a consequence of this theory. Put another way, the instant you ‘invent’ a new math, you’ve also discovered a part of the universe. This troubles me but Goedel dealt with this a little bit with his ontological proof. It obviously has disturbing ramifications.
On the bright side, it should be possible to introduce code on a local level that allows one to access the equation and tinker with it. Work-arounds, back-doors, negating features, isolation of equation fragments and moving them to other parts of the equation et al.
Another implication which is not so disturbing: there is no such thing as a simulated universe. Any ‘simulation’ that functions as such IS in fact what it ‘simulates’. The ‘digital creatures’ within the ‘Universim’ you bought at Radio Shack (Kids! Get 100 billion galaxies for only $9.95!) are alive. Especially from their local perspective. Their local functions- their mathematical electrons and quarks are entirely real to them and solid as rocks so to speak.
But that brings people back to the whole god thing and they get angry. I think this is because they want the universe to be a specific way but we won’t get very far by demanding reality bend to our prejudices. Yeah, the idea does imply something big that we don’t understand or have difficulty understanding. But it doesn’t have to be voodoo if that’s the way it really is.
Go ahead, laugh. I’m used to it. I’ve been walking around with this idea tormenting me and delighting me all my life. Not gonna stop now.
I’ll make one more prediction: This idea will not go away.
by Rob Falgiano
I have no interest in laughing at your ideas as I find them quite interesting and plausible. All thoughts are energy. They leave us and they head out into the quantum universe. Which is why someone can feel you thinking of them at any distance and without the travel time of light. Synchronicity is the acknowledgment that the universe is simultaneously mathematical and mystical and that we can live at a higher level of awareness of its machinations. I find this very satisfying and I have found it to be absolutely true in the practice of my own life. When I synchronize good things happen all around me like harmonic waves of sound lining up to make beautiful music. Aligning the waves…
by Tom B.
Mathematics must go hand-in-glove with data. Bad or insufficient data renders even the best math either useless, less useful, or downright misleading.
by cosmowrench
Galileo Galilei – “Mathematics is the language with which God has written the universe.”
by Max Tegmark
I love the full version of Galileo’s quote:
“Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these one is wandering in a dark labyrinth”.
If you’re interested in these ideas, you’re welcome to join the discussion on my Facebook page: http://www.facebook.com/pages/Max-Tegmark/461616050561921
by Editor
Thanks for the invite, Max! I’m there.
by Singularity Utopia
Thankfully the religious taint upon thinking is less prominent in the year 2013 than it was in the era of Galileo, thus we can disregard Galileo’s flowery language, possibly written to appease religious tyrants, regarding how “Mathematics is [allegedly] the language with which God has written the universe.”
Most people today realize God does not exist, God has NOT written anything regarding the universe, there is no intelligent design whatsoever, there is no God. The only things which are intelligently designed are things humans are have very deliberately designed.
Smart people such as Einstein or Galileo are not Gods. What I mean is that a smart person can also at times be idiotic thus not every utterance by Einstein or Galileo is gospel, such people are more than capable of saying idiotic things such as “God is a mathematician.” Sadly Einstein did not live in an age where it was possible to read The God Delusion by Richard Dawkins. If Einstein had read that book he might of said God is a delusional belief system for people who are afraid to confront reality, instead of stating God is a mathematician.
by SmartAndSober
It is observed that complex structures can spontaneously emerge.
Examples: Biogenesis on Earth (non-living molecules by chance gather together and become the first lifeform), evolution of life from low intelligence to high intelligence, self-healing, self-balancing ability of ecosystems and Earth’s biosphere.
Non-natural examples include complex structures in cellular automata.
I recommend a encyclopedic website on Conway’s Game of Life http://www.conwaylife.com/wiki/Main_Page
by Jack Reeve
God… what a concept…
by Jack Reeve
I hope transition from stone-age mythology to modern science follows the same curve as Ray’s line to the singularity. That, in and of itself, would go a ways toward eradication of a litany of global woes, as any secular thinker can readily see.
by SmartAndSober
“… thus we can disregard Galileo’s flowery language, possibly written to appease religious tyrants, ”
I guess Galileo must felt frustrated for the religious people’s close-minded-ness. Even by using words familiar to the religious people (being diplomatic), he cannot make them abandon their outdated beliefs.
Being diplomatic, instead of directly agressive confrontation, is useful not only in the 16th and 17th century, but also in today’s world.
For example, some problems we have to solve in the 21st century would be:
To promote cloud-computing science projects such as Folding@Home
To convince the paper-hoarders (the science paper publishers) to emancipate the papers they hoard.
To promote science/technology education in developing countries.
To de-religious and disband the strongly religious groups and countries (like the Middle-Eastern fundamentalist countries) and also ideology-based dictatorships (like N Korea).
To promote space mining (for example, asteroid mining) and space colonization.
by MatthewQ
What if you don’t do facebook?
You got something else somewhere else I can access this?
by Jjkiam
Thanks for initiating such a lively response with your article and for contributing the rest of Galileo’s quote. While not religious it is amusing to see how defensive some of the atheists in the crowd get when seeing euphemistic uses of the word God in a description of reality. To those I simply say Don’t worry Be Happy :-)
by star0
From an interview with Steven Strogatz that I’ve always liked:
Arbesman: When did you first realize that mathematics was not simply another topic in school, but that there was a real pleasure in figuring how it explained the world?
Strogatz: It came in the form of an epiphany. In my first science class in high school, our teacher, Mr. diCurcio, asked us all to measure the period of a pendulum, the time it takes for the pendulum to swing back and forth. He gave each of us a little pendulum and a stopwatch. The pendulum could be lengthened or shortened in discrete clicks, and our assignment was to set the pendulum to a certain length, and then let it swing 10 times back and forth, meanwhile timing how long it took to make those 10 swings. Then we were supposed to repeat the measurement for pendulums of different lengths, and to plot our results as dots on a piece of graph paper, with the length of the pendulum on the x-axis and the time required for 10 swings on the y-axis. It was intended as a lesson in how to use graph paper, but it became clear to me after plotting the fourth or fifth dot that a pattern was emerging. The dots were falling on a curve. I recognized its shape because I’d seen it in algebra class. It was a parabola — the same shape that water makes when it comes out of a drinking fountain. I felt a peculiar chill, an enveloping sensation of fear and awe: this pendulum knows algebra! In that moment I suddenly understood what people meant by “laws of nature.” It was a moment from which I’ve never really recovered. It felt like I was being let in on a secret. There were beautiful, hidden patterns in the world, patterns you couldn’t see unless you knew math.
by SmartAndSober
Thanks for sharing your idea, star0. I have that feeling of awe toward mathematics, too.
Some children feel *bored* in mathematics. Perhaps it is because they had not yet learned the *pattern* that interests them.
(Jurgen Schmidhuber, an expert in machine learning, had discovered a “Formal Theory of Fun”.
Jurgen Schmidhuber’s site http://www.idsia.ch/~juergen/
A KurzweilAI article on his research and theory
http://www.kurzweilai.net/how-bio-inspired-deep-learning-keeps-winning-competitions).
I believe that, in the future we will discover that there is a mathematical/physical rule for *almost everything* in the universe.
But, there are rules that we cannot (and and will never) know for 100% sure-ness.Instead, we can only create a statistics/probability based theory.
E.G. We can never know an *absolutely true* rule for predicting prime number distributions, because to do that we need to calculate all primes, but there are infinite of them.
The calculation will take *literally* forever (unless we find a way to do *infinite* computation in a *finite* amount of time).
Statistical rules (for predicting prime patterns) do exist.
Examples include the *twin prime cojectures* (many of them, please see http://en.wikipedia.org/wiki/Twin_prime )
and the *apparent* patterns in the “Ulam Spiral” (2-dimensional graph of all prime number, please see http://en.wikipedia.org/wiki/Ulam_spiral )
by Editor
star0: Thanks for that inspiring quote. Brought back fond memories of discovering the sheer beauty of algebraic geometry and calculus by making plots on graph paper.